Check the differentiability if `f(x) = min. {1, x^(2), x^(3)}`.

Explanation

To check the differentiability of the function \( f(x) = \min\{1, x^2, x^3\} \), we will analyze the function piece by piece and determine where it is differentiable and where it is not.

### Step 1: Identify the pieces of the function
The function is defined as the minimum of three functions:
1. \( y = 1 \)
2. \( y = x^2 \)
3. \( y = x^3 \)

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